Review:Given

Find

Find

Looking Ahead – Challenge:Graph the points:

A (-2,-3)B (-1,1)C (3,5)Connect the points from A to B to C.

Math 93: Kathy Conway Instructor

32)( xxf 1)( xxg

))(( xgf)(

1xf

§ 8.4

Composite and Inverse Functions1. Form Composite Functions2. Verify Inverse Functions3. Find the Inverse4. Horizontal Line Test5. Graphs of Inverse Functions

Blitzer, Introductory and Intermediate Algebra, 3e – Slide #3 Section 8.4

Graphs of Inverse Functions

f(x) x y

A -2 4

B -1 0

C 5 1

Blitzer, Introductory and Intermediate Algebra, 3e – Slide #4 Section 8.4

Graphs of Inverse Functions

f(x) x y

A -2 4

B -1 0

C 5 1

f-1(x) x y

A 4 -2

B 0 -1

C 1 5

Blitzer, Introductory and Intermediate Algebra, 3e – Slide #5 Section 8.4

Graphs of Inverse Functions

Blitzer, Introductory and Intermediate Algebra, 3e – Slide #6 Section 8.4

Graphs of Inverse Functions

Blitzer, Introductory and Intermediate Algebra, 3e – Slide #7 Section 8.4

Graphs of Inverse Functions

Review:y = f(x) is a function if it passes the vertical line test.The inverse of f(x) is a function if it passes the horizontal line test.

New:It is a One-to-One (1-1) function if it passes both the vertical line test and the horizontal line test.

A 1-1 function is a function in which no two different ordered pairs have the same second component. Only 1-1 functions have inverse functions.

Blitzer, Introductory and Intermediate Algebra, 3e – Slide #8 Section 8.4

Inverse Functions

Graphs of f and TThere is a relationship between the graph of a one-to-one function, f , and its inverse, . Because inverse functions have ordered pairs with the coordinates reversed, if the point (a,b) is on the graph of f , then the point (b,a) is on the graph of . The points (a,b) and (b,a) are symmetric with respect to the line y = x. Thus, the graph of is a reflection of the graph of f about the line y = x.

1f

1f

1f

1f

Blitzer, Introductory and Intermediate Algebra, 3e – Slide #9 Section 8.4

Some reminders…

Note that:

1f means f inverse and not f to the negative one power

Blitzer, Introductory and Intermediate Algebra, 3e – Slide #10 Section 8.4

Inverse & Horizontal Line Test

Assignment:1. Math Lab Plus = My Math Lab (MML):

8.4 #1-24

Due Thursday, October 18 at beginning of class

2. Homework 8.4#2, 6, 16, 18, 26, 30, 32, 38, 42, 48

I will give you the answers tomorrow and we will discuss questions so bring completed homework tomorrow, but

Due Thursday, October 18 at beginning of class